Modern Robotics, Chapter 3.2.2: Angular Velocities

This video introduces 3-vector angular velocities and the space of 3x3 skew-symmetric matrices called so(3), the Lie algebra of the Lie group SO(3). Any 3-vector angular velocity has a corresponding so(3) representation.

This video is a brief summary of material from the book, and it is not meant to stand alone. For more details, such as an explanation of the notation, please consult the book and the other videos.

[gzitterspiller]

You sir, deserve much more views... great book. I am not into robotics, I am more an structural engineer (finite element method) but I used this book for theory of machines and it was great, nothing can touch this book, everything is well put togheter, enough proofs, good drawings, etc... 10/10

[AirAdventurer]

This is a fascinating introduction to Lie algebras, in particular, of course so(3) = thank you!

[markkennedy]

Hi,

I was hoping you could answer something about the angular velocity vector:

When I take an angular velocity omega in 3 space and decompose it into its x, y and z components, omega_1, omega_2 and omega_3 respectively, we expect the magnitude of the angular velocity vector to be: |omega| = square root of

However, if you think about the rotation of a body described by the omega vector:

Let's say it does one full rotation in 1 second. Physically, the projections of this rotation onto the yz plane, xz plane and xy plane correspond respectively to the x, y and z components of omega above and each of these projections (of the body onto the respective planes) all undergo one full rotation in 1 second also.

So, on the face of it, the angular velocities of each of these components are on average (over one rotation) the exact same as the magnitude of the angular velocity of our vector omega (if we trace out the motion of the body itself and the motions of the projections of the body):

|Omega| = omega_1 = omega_2 = omega_3

This contradicts the decomposition above.

Can you explain what's going on here and what assumptions above are false.

I would be very grateful if you could offer help with this as I can't get answers anywhere else. I'm interested in fitting the mathematics with the relevant physics.

Thanks.

[diodin]

A rotation matrix R has no time, where comes the angular *velocity*?

[alexfish]

What does this notation mean when in brackets? R'_sb = [X'_b Y'_b Z'_b] or M = [M_1 M_2 M_3] where 123 are subscripts?